In Hiscox movement 1513, two equal pivoted links keep a pair of ruler bars parallel. Each moving pivot follows a circle about its fixed partner. Calculate the longitudinal shift, perpendicular separation and arc travel for an entered opening angle.
Transferring a line direction
The two equal links let one ruler bar move while staying parallel to the other. Holding one bar stationary preserves a reference direction as the second is repositioned. The calculator separates the perpendicular distance between the bars from the curved distance traveled by a pivot.
Hiscox 1513 Pivot-Path Calculator
Enter equal bar pivot spacing, equal link length and opening angle. The worksheet reports exact translation components and pivot arc travel.
Equation Used
- The two ruler bars are rigid and have equal corresponding pivot spacing C.
- Both metal links have exact equal pivot-center length L.
- All four joints are perfect coplanar revolute pins.
- The opening angle is measured from the aligned-link reference and theta is converted to radians for arc length.
- Tolerance, clearance, friction, compliance, wear and drawing accuracy are excluded.
The moving pins follow circular arcs while the upper ruler remains parallel. Numerical results describe the entered angle, identified by the dashed selected-position bar.
Hiscox movement 1513
Hiscox describes movement 1513 as a parallel ruler formed of two bars pivoted to two pieces of metal of exactly equal lengths between pivot centers and at equal distances on the bars. Those four pivot centers form a parallelogram.
Each moving pivot follows a circular arc of radius L about its fixed pivot. Because both link vectors are identical, every point on the moving bar receives the same translation and the bar does not rotate.
Parallel-line transfer
European Patent EP0168948A1 describes the established use: linked straight edges can be moved closer or farther apart without changing their relative orientation. German Patent DE3720431A1 documents a two-plate example with 400 mm plates, approximately 90 mm arms and 170 mm pivot spacing.
Those documented dimensions provide the defaults here; they are not performance limits or manufacturing prescriptions.
Translation and pivot arc
The pivot arc uses theta in radians. The moving bar remains parallel because corresponding pivots share the same displacement vector.
Declared geometry example
For C=170 mm, L=90 mm and theta=50 degrees, longitudinal shift is 57.85 mm, perpendicular separation is 68.94 mm, moving-pivot arc travel is 78.54 mm and ideal edge-angle error is zero.
What the ideal movement does not predict
Physical accuracy depends on measured link mismatch, pin and bore geometry, in-plane and out-of-plane clearance, member stiffness, wear and how the instrument is handled.
The circular-path and parallelism results assume equal links and perfect pivots. Errors in an actual instrument require its measured geometry and clearances rather than a universal tolerance rule.
Movement-1513 questions
Why is the pivot path circular?
Each moving pivot is the end of a rigid link rotating about a fixed pivot.
Why does the ruler bar stay parallel?
The equal links impose the same displacement at both bar pivots.
Is arc travel the straight-line separation?
No; arc travel is distance along the circular path, while separation is its perpendicular component.
Does zero ideal error specify a physical tolerance?
No.
Parallel-ruler references
- Gardner D. Hiscox, Mechanical Movements, section XVII, movement 1513: two bars, two exactly equal pivot links and equal bar pivot spacing.
- German Patent DE3720431A1: two parallel plates, parallel arms and documented example dimensions.
- European Patent EP0168948A1: linked parallel straight edges whose distance changes without orientation change.
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